This council was located somewhere in the county of Surrey. It exercised a certain amount of rights over the people in its dominion, which included the Dursley family. This council was among Vernon Dursley's favourite things to complain about.

Behind the scenes

It is not clarified what sort of council Vernon is referring to. It could be the parish council for Little Whinging (assuming that they are part of the approximately 30% of the population with one), the district council, or the Surrey County Council.